Skip to main content
Log in

A modified Bernstein-technique for estimating noise-perturbed function values

  • Published:
CALCOLO Aims and scope Submit manuscript

Abstract

A Bernstein-type improvement of the Bienaymé-Chebyshev inequality is presented for evaluating a general class of noise-perturbed functions. This result can be applied in the course of solving stochastic optimization problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. M. A. H. Dempster, ed.,Stochastic Programming, (1980), Academic Press, London-New York.

    MATH  Google Scholar 

  2. W. Hoeffding,Probability inequalities for sums of bounded random variables, (1963), J. Amer. Statist. Assoc.58, 13–30.

    Article  MATH  MathSciNet  Google Scholar 

  3. P. KallA. Prékopa eds.,Recent Results in Stochastic Programming, (1980), Lecture Notes in Econom. and Math. Systems179, Springer, Berlin-Heidelberg.

    MATH  Google Scholar 

  4. M. Okamoto,Some inequalities relating to the partial sum of binomial probabilities, (1958), Ann. Inst. Statist. Math.,10, 29–35.

    Article  MATH  MathSciNet  Google Scholar 

  5. J. Pintér,An improved Chebyshev-inequality for function value estimates by Monte Carlo techniques, (1983) (In Hungarian) Alkalmazott Matematikai Lapok,9, 93–104.

    MATH  MathSciNet  Google Scholar 

  6. B. T. Poljak,Nonlinear programming methods in the presence of noise, (1978), Math. Programming,14, 87–97.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pintér, J. A modified Bernstein-technique for estimating noise-perturbed function values. Calcolo 22, 241–247 (1985). https://doi.org/10.1007/BF02576496

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02576496

Keywords

Navigation